This paper describes an efficient, complete approach for solving a complex allocation and scheduling problem for Multi-Processor System-on-Chip (MPSoC). Given a throughput constraint for a target application characterized as a task graph annotated with computation, communication and storage requirements, we compute an allocation and schedule which minimizes communication cost first, and then the makespan given the minimal communication cost. Our approach is based on problem decomposition where the allocation is solved through an Integer Programming solver, while the scheduling through a Constraint Programming solver. The two solvers are interleaved and their interaction regulated by no-good generation. Experimental results show speedups of orders of magnitude w.r.t. pure IP and CP solution strategies.